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Mathematics 8
Unit 1: The Number System & Exponents
Part I: What should students know and be able to do by the end of this
part of the unit?
8.NS.A Know that there are numbers that are not rational, and approximate them by rational
numbers.
8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every
number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually,
and convert a decimal expansion which repeats eventually into a rational number.
8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate
them approximately on a number line diagram, and estimate the value of expressions. For example, by
truncating the decimal expansion of the square root of 2, show that the square root of two is between 1 and 2,
then between 1.4 and1.5, and explain how to continue on to get better approximations.
8.EE.A Work with radicals and integer exponents.
8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x 2=p and x3=p,
where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small
perfect cubes. Know that the square root of 2 is irrational.
8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
For example, (32)(3-5)=3-3=1/27.
8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very
large or very small quantities, and to express how many times as much one is than the other. For example,
estimate the population of the United States as 3X108 and the population of the world as 7X109, and
determine the world population is more than 20 times larger.
8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both
decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for
measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading).
Interpret scientific notation that has been generated by technology.
Part II: Developing Essential Questions
Enduring Understandings
Essential Questions
Mathematics 8
Unit 2: Geometry
Part I: What should students know and be able to do by the end of this
part of the unit?
8.G.B Understand and apply the Pythagorean Theorem.
8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world
and mathematical problems in two and three dimensions.
8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8.G.A Understand congruence and similarity using physical models, transparencies, or geometry
software.
8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about
the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of
triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears
to form a line, and give an argument in terms of transversals why this is so.
8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations:
1a. Lines are taken to lines, and line segments to line segments of the same length.
1b. Angles are taken to angles of the same measure.
1c. Parallel lines are taken to parallel lines.
8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures
using coordinates.
8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from
the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a
sequence that exhibits the congruence between them.
8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the
first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional
figures, describe a sequence that exhibits the similarity between them.
Part II: Developing Essential Questions
Enduring Understandings
Essential Questions